Class Note for BINF 709 at KU
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Date Created: 02/06/15
Outline Examples of biological networks Problems for Systems Biology Molecular basis elements of networks Experimental techniques Network representations Examples of biological networks Molecular interactions Functional interactions and regulation Metabolism and chemical networks Genomic data as networks neuronaL mechanical physiological Examples of biological networks 0 Molecular interactions Examples of biological networks 7 Proteinprotein r i lquot interactions proteins 5000 interactions 7000 Databases BindDB MIPS DIP fquot l39ilx i t A comprehensive analysis ofpl oteiupt otem interactions in Scerevisiae Nature 2000 6237 UelZ P et a1 Ex perlmontal methods Reporter gene Yeast two hybrid Computatlonal met hods Gene fusion 511 D D D 5P2 G D CD Spa GD ED SP4 Cl D D D Genomic c context 3 lilitillll 53935 However the most widely used systems remain the yeast twohy brid system and affinity purlflcations The idea behindtheyeastm39ohybrld system is simple see figure part aln the most common variant a bifunctlonaltranscription factor usually Grill is split into its DNAbinding domain DBD and its activation domain LADi Each segment lsthen fused to a protein of i nterest X and Yl and if these two proteins interact the activity of the transcription factor is reconstituted lite system has been scaled up and applied i n genomescale screens 39 39 For affinity purification see figure part b a protein of interest bait is tagged with a molecular label dark purple in the figural to allow easy purification The tagged protein is then co puriflecl togetherwith its i nteractlng partners W Zlua39hlch are usually identified by mass spectrometry Thisstrategy has also been applied on a genome scalew39 Af nity column A 39inity puri c ations ea i SP1 5 Sp SP4 SpS Sp Coevoluti o n Protein protein interactions can also be predicted computationallyavith accuracies that are comparable to those of large5c ale ex periments Most of the computational efforts are based on the comparison of complete genome sequences For example if two proteincoding genes are found to be separate in one species Sp and fused to form a single gene in another see figure part C a physical interaction is probablem IEither methods consider onlythe two proteins of interest X and Y For example theywould precil ct thatthe two proteins lnterac t or are functionally related if they show a similar pattern of evolution across several species see figure part ii inpui upstream reguluwrs Outpul substmial e emr Examples of biological networks 1 Mayo site 7 Docking lnlomclluns oq Modular domain A c Scmuldkladaplors nglilylntsg med cnmiyiic and reg Lll moly functions High Low 5 Law H igh Separabls mandamin components median connectivity and regulsllon of dlve rse cuisiyuc iiri ils i odulc an indcpcndcndy folding domain that can carry out i simplc Funcdon Docking interaction bem ecn a catalytic domain and i partner protein that docs not involvc The audit site Sca old aprottin that binds and colom zcs duct or mom members of a catalytic pathway Adapter protein that binds and colocalizcs two mctiona y inner min 3 mcm hem ofa catalytic pathway Evolmbility39 the ability Ufa Sijttm to gen crate new heritablc traits or behaviors through genetic changes wm 7 mm M m Wtw AWN pwmww amwx m cyrmunn gt m Lkw n n a n a s i Kwascnur ilmmm 4gtemvau an m 5mm rm x 9 mm 1 mm CANCER IS CAUSED BY THE BREAKDOWN OF SEVERAL 9 MORTANT NET390RJ 91LAI GI ARD AGAINSL UNCONTROLLED PROLIFERATION Adaptor NC I 2 muquot Cuk Crkl Ema 13mg Bank 3W SLAP m Sultana Shm 2 34 ia ame MIST SUM 391 SL975 55qu5 65 Kinasas F143 For m Sm Csk um 5 an NilInk J liLwall Fm 3939 Elk Sums zapm an a FTPNE STAN 8 Ghl Chm CHO PlKlRS FIKBR1 2 PUle EHIFl M11 Nara ii rm Elk real In Hm i M 1t Wm M2 Signal ngt a un SHmIAB AH scams CJSH V sacsaway I3939 5NDIEI 7 2L BHZDZA HsHm 4 5H2mn3 e rim ID 1 3 AP5Lrh5H23 5 MP1 39I 531951545 3H33s2 1 i TILmm THEE H154 TN51 Supt i HMEM EHEHHRJ BOMB quot1139 WWZJ 41an Phnsphatasu 111 ij Tnanacri plinn i I Uhiqultlnadnn Elfl mifLQ Phosphoiiwpisl 5mm Messenger Signallng Cytmkelmal Regula on a 6 l Chmmalin Rumud lml V V he Small GTFuu Signaling 39 JIA IL Hm WG34 543 xuodulc an indcpcndcntly folding domain that can many out 1 simple mc cm Docking intcrac on btfwttn a catalytic domain and a partly prnrcin that docs not involve the amiw site Scalfold a promin that binds and colom lcs three 0139 mam mcmbcrs of a catalytic padzway Adapter protein that binds and colom xcs two fLutlJztiotnaLlr intcracting mtmbcrs of a catalytic pa nwgr Evolvnhility Eh ability of 1 5551mm to gentran new hcritablc traits or behaviors nrough gcncu39c changes pm 5 mmwwn mum m mm My rmmn WWW rwwwk mm m M mm dom39umuhhc Wm nnunm vl m m uwly m 5m mm mm m WNW an Mm Alon Muk m m puma w m m upwml u mm m m mmmm mum n my sm 0 ltprununt m mum mm m m alga lhukrwuc m WWW m m mu mm 7 m WWW mnam vumlmg o m m u mm m ngm a m mm mmquot m mmm nnwvrk mmmm v m Sm 40mm mum AMYNIEV Wu Myo39r I aquot um um Hl cmmkd M m WWW mm mm u m um um WWW Wu quotumquot mum n ma my mmva W u mummy mm W rtuvhvral m m M mm m mmm m mm 1 mm mm mm mm m m mm mm M m way Wm WM m mmmn m mum mm m WWW Wm mu m annual M m w mm m mner w mm uul m m rm pnlugc umpu vhmvimlun mummmwm nol w mummm pm mmuuwn Plateletderived growth factor PDGF receptor signaling H I W 7mm RasRaf signaling llgand ligand bindlng extracellulav domam 4 lecspmr dimevizalion receptor tyrosine aulophcsphnrylalioy Cell Membrane 39 Iransmembrane unmam lunacenmav Domam GTFase Activaling Has pathway zuuvaxinn quotmm RastAPs gt p1 ZDGAP Grb2 39 neurolibmmin Nucleus Nuclear Gene Regulation Mitogenactivated protein kinases MAP kinases signal transduction Extracellular valm rams uv sums Dsmulm Snack rm munmmmvy mm mm 5 v raman Amsumynn emu uv m as ecxn y 7513mm mire MAFSKS MAP3K1 makn W A Jki mat W quot l a quotm WM 1 PM wn a W MM mm mums rimquot me was my msz g E lt s E v mm mpm39 mm mm min 43K mgr in 39 W V W mm mm WW WW 9 H mpmxz mmxg quotma v mxquot ps KA upsmz 5515mm m 1 mpmpxa new mum s t W MKsz mm quotmm at gm 7 mm mm m M mm 1 E 315 39 r r ELFK uu 2 E quot 39 Hymanm ma r 10 AKTPl3 kinase signaling H JakSTAT5 Signaling Erythropoietin Receptor JakISTAT12 signaling Interferon alpha receptor Wnt signaling NFkB signaling mm 5mm HedgehogEli signaling 15 SMAD signaling TGFbeta ac 39 bone morphogenetic proteins TGFB Signaling Pathway 155p summuy ligands 8MP sub0mm iigands TsrnsAcrivinsNadais EMP2 1 MIS Iypel A 9 quot B39 lypuil man in r recapwr quotMWquot 9 lecevlar RI SARA xr A smdzr 1 Suin7 vi ma l m Smum Gm 5mm SmadilsB AK swans l AB V SmaM m y 39 39 39n common SmadzJ Saudi515 5mm TGIF CE CBP V Smadm SmudIEE 5mm TF n 7 5mm 7 Smadzlz patina TF3 Targal Gem Targel Genes Smadllsm perms 11 mm V53 Mix 2 35 Va mm OAZ ums mm Lsmcr No al mm le2 Smaus Schwinn cam van cam m2 Swan mm W25 Notch signaling h x 22253 0 RAM Ilumam Ankynn mum l39mmcnplmn Icnvumr down pmmgm o DSLdunmn Meullnpmldme dommn Dmmanmdnmmn cw denmam Mama 0 urL rmmuu mmngmm HMon N Hiimm nu law a quot ammawa 6 m f 39 Gen Tmnscnpuan a domain ms Checkpoint Cell cycle regulation mls chmpolm GH Camcl mmuum DNA ramq Rnnlrcuive sonscene gum who Ulrl mm mm A summa Vim inclv Gmwm mm Whilan um 39 1 39quotgt Utaunruan m 7 3 mumquot u M am uan ems vdm m Ear1mm um um mm m mm mu m a GZM damage checkpoint Cell cycle regulation GM DNA Damage Checkpoint f Crl39llca ll y Short J A Telomems Nuclear Expmi Ublqullinarlon Nuclwlur M Sean33mm Fish 391 39 1 u zquot 1 wr V 153 Stublllmlnn lamI2 p53 3 r 4 Nude r I mp F xfy j39rgpqlquot mui 1434 quotunmet p53 an E9 if a 5c r W at fr ea Ubiquitlnulim sf3quot 70 Apoptosis Inhibition Inhibition of Apoptosis AF DFTGSIS 71 Apoptosis activation Death Receptor Signaling Death Receptor Signaling APDQU m F u Tm quot mar APO2U L 39wa h l Eu 7 c quot 1 L on PI 35 Mat 1 4 quotAP Cazpasa cum r J lndmmmjnm cell dulh a mm mm QWI NH 3 mini 39Achin an mm 1mm Arman l Cull shrinkage Mmbrano numbing DNA hagmnlnllon cnmmlnn condom v A F DPTCISIS 77 Apoptosis Control by Mitochondria Mitochondrial Control of Apoptosis Fm 39Dngllh Stlmull Sunnia Fm Withdrawal Survival Factura r Gmwm Factors Wakinequc l l 1 1 1 l c l I 1 i l 39 y S E x mm mumgm r may r l i nd 5 tag 1 F manna tying nequontmllan In napalm an in a cmF V39l39 Emma mm 339 3 m APDPTOSIS Ganglion Stress p53 Ham 7 Toll Receptor Signaling Exlmoawlar aw LAwJ uuu am My mm M um m a v m unnucmmmpm Damriu calla mum Emmm himnmallai mill 3 Protein Coupled Signaling Gpmhln coupled mupiaismnnungin MAPKIERK mmninnau 25 Fc Receptor Signaling 7s T cell antigen receptor signaling l mmu Ion mam incrmae nene expm an by Imumng why their regulatory amuences 39 u 39 27 B cell antigen receptor signaling B Gail Antigen Renewal Slgna ng fir 9 L n 3 v L ma 1 I Q 7 1 5 W a W a r l 9 9 6i 5 l a k 239 l V n 1 Thaw 9 a In i 6 5 i 2 1 438 mi dun Mi iii1 mi 95 bu EH mi L W J mausc RIF39TIQN 7R Examples of biological networks Functional interactions and regulation Examples of biological networks Regulation Wave Mm Sea 5 m m 4 m am Stu stem Sum ms m Fan Examples of biological networks Metabolism and chemical networks Biochemical reactions Biochemical metabolic reactions Chemical engine Determines cell physiology Similar in all organisms KEGG EcoCyc Metabolic Fluxes 91 ZJZDGS HST msnmuc 170quotst Metabolic Pathway msnmuc pmmms Examples of biological networks Genomic data as networks Problems 1 Derive networks from experimental data design of experiments 2 Structure of the network descriptive functional 3 Dynamics steady state response computation fluctuations 4 Evolution cell s point of view Kitano s milestones understanding of structure of the system such as gene regulatory and biochemical networks as well as physical structures understanding of dynamics ofthe system both quantitative and qualitative analysis as well as construction oftheorymodel with powerful prediction capability understanding of control methods ofthe system understanding of design methods of the system References H Kitano Systems Biology a brief overview Science 29516622002 H Kitano Computational Systems Biology Nature 420206210 2002 Structure of biological networks Outline Review of Lecture 1 Representations Basic concepts Real vs random networks Biological questions Representation Graphs digraphs weighted graphs Bipartite graphs Hypergraphs Stochiometry matrices NE N5n1 n2 nN Eel 82 8M ekni n3 Cons rr39oins no duplico re edges no loops e rc Eg Nodes pr39o reins Edges in rer oc rions Graphs is NE Mutligraph N5n1 n2 nN Ee1 e2 eM y ekni n3 duplica re edges Eg Nodes pr39o reins Edges interactions of differen r sor r binding and similari ry Hypergraphs 39NE N5n1 n2 nN Eel 82 8M exnil J nk Cons rr39oins no duplico re edges no loops e rc Eg Nodes pr39o reins Edges pr o rein complexes Directed Hypergraphs 39NE N5n1 n2 nN Eel 82 8M exnil quotJ I nk nI Eg Nodes subs rances Edges chemical reactions A B gt C D XA B I C Dm Bipartite graphs substances reactions X K X 39 Bipartite graphs substances reactions 39gtlt 739 Bipartite graph Substrate graph 03 02 03 02 N02 gti NCE N02 X No3 Fig 2 meanon projection fmm a bipartite graph to a substrate graph Directed Graphs 39NE N5n1 n2 nN Ee1 e2 eM L ekni nj 0 v Cons rr39ains quotno dupheaJFe edges no loops e rc Eg Nodes genes and Their products Edges from A To B gene A r39egula res expression of gene B Flux Balance Analysis Boundary Steady state Mass Balance momma r1 RA 1 0 0 0 0 0 0 39RA r1r4 r2 r30 S V b 1 1 1 1 o o o o r2 r5 r6Rc 0 1 0 0 391 391 0 2 RC r3r5 r4 r7RD o o 1 391 1 o 391 RD 0 0 0 0 0 1 1 RE r1 r2 r3 r4 r5 r6 r7 r6r7RE v Tra nspo rta tion fluxes H J lntemal fluxes Summary Different problems gt different graphs Basic concepts Degree components path length diameter Clustering coefficient Centrality and betweenes Random graphs giant component component size distribution Basic concepts Nodes pr39o reins Edges in rer ac rions Node degree Compo nen rs Shorquotres r pa rh Diame rer39ltShorquotres r Pa rhgt 5E5 Basic concepts Nodes pr39o reins Edges in rer ac rions Node degree dk Compo nen rs Shorquotres r pa rh Diame rer39ltShorquotres r Pa rhgt if Basic concepts Nodes pr39o reins Edges in rer ac rions Node degree dk Compo nen rs Shorquotres r pa rh Diame rer39ltShorquotres r Pa rhgt if Basic concepts Nodes pr39o reins Edges in rer ac rions Node degree dk Compo nen rs Shorquotres r pa rh Diame rer39ltShorquotres r Pa rhgt 5E5 Basic concepts Nodes pr39o reins Edges in rer ac rions Node degree Compo nen rs Shorquotres r pa rh Diame rer39ltShorquotres r Pa rhgt Basic concepts Nodes pr39o reins Edges in rer ac rions Node degree Compo nen rs Shorquotres r pa139h Diame rer39ltShorquotres r Pa rhgt 3 Basic concepts Nodes pr39o reins Edges in rer ac rions M Node degree Componen rs o Shorquotres r pa rh 2 Diame139er39ltShorquotres r PaThgt Z ZZZJ NN1ij1N Basic concepts Clustering coefficient of node i 39 0y Ci 2Eikiki1 fraction of realized interaction between the neighbors of Triangles that include i kiki1 Clustering coefficient of graph 6 C 1NIZNCi Basic concepts CenTraliTy y BeTweenness of nodek Sk gt gk 2 U 39 z39j1N 5 0 where 5U is The number of SHORTEST paThs from i To j siJ k The number of such paThs ThaT 90 Through k ed em 9 gm 2 U z39j1N Sz39j COMPARE REAL NETWORKS WITH RANDOM ONES in all these parameters WHAT IS A RANDOM GRAPH Wagner et al 2000 Barabasi etal 2000 AB model Robustness ON THE EVOLUTION OF RANDOM GRAPHS by F limbs and A RENYI Institute of Mathematics Hungarian Aeedemy of Scienres Hungmy 1 De nition of a random graph Let Enquot denote the set of all gmphs having n given labelled vertices VtV2 39 V and N edges The graphs considered are supposed to he not oriented without parallel edges and without slings such graphs are sometimes called linear graphs Thus a graph belonging to the set Ems is obtained by choosing N out of the possible edges between the points Vi V2 quot39 V and therefore the number of elements of EM is equal to 21 A random graph 139v can be de ned as an element of EM ehosen at random so that each of the elements of Ey have the same probability to be chosen namely llgl There 15 however an other slightly different pomt ol View which has some advantages We may consider the forma Lion of 1 random graph as a stochastic pram de ned as follows At time 1 we choose one out of the 3 possible edges cenneeting the points V V V each of Ihcsc edges having the same probability to he e hosen let this edge be denoted by e At time 22 we choose one of the possible 1 edges different from at all these being equiprobable Continuing this process at time zk1 we choose A use m 1 meme e4quot lmmmt mm tho Mm m es elven Paul ErdOs and A R nyi On The evolu rion of random r39ahs Magyar Tud Akad Ma r Ku r In r Kozl 5 1960 1761 Random graphs ErdosReyni start with N nodes pick two at random and connect them exclude loops and double edges continue ti M edges are formed Degree ltkgt 2MN k distribution Poisson diameter Z I logN clustering coef C 0 Random graphs ErdosReyni P2MNNI c2MN 181 Theorem 54 of 1 Theorem 1 Consider an EMK39A39s Renyi random mph 0111 Set 1 017 xed 6 gt 0 Study n gt 00 limits Assertions mid with 10117114 1 05 n gt 00 a Ifc lt 1 the lamest armponem size is at most ECLF logn b If a gt 1 were is a unique yitmt mmponem with 1 01871 m39rtiaes where I c gt 0 solves 5quot 1 The seamd39 lamest armament size is at most Tiff log n The evolu rion of random graphs Gnp O cn 1 n c39 n log n n w log nn wgtT The evolu rion of random graphs Gnp O disjoint union of Trees cn 1 n c39n log n n w log nn wgtT The evolu rion of random graphs Gnp O disjoint union of Trees Cn cycles of any size 1n c39n log nn w log nn wgtT The evolu rion of random graphs Gnp O disjoint union of Trees Cn cycles of any size 1n The double jumps c39n log nn w log nn wgtT The evolu rion of random graphs Gnp O disjoin r union of Trees Cn cycles of any size 1n The double jumps c n one gian r componen r others are rr39ees log nn w log nn wgtT The evolu rion of random graphs Gnp O disjoin r union of Trees Cn cycles of any size 1n The double jumps c n one gian r componen r others are rr39ees log nn Gnp is connec red w log nn wgtT The evolu rion of random graphs Gnp O disjoin r union of Trees Cn cycles of any size 1n The double jumps c39 n one gian r componen r o rhers are rrees log nn Gnp is connec red w log nn wgtT connec red and almos r regular nZgtIlt OOltugtNm mm ZmltltO Am ltltI ZgtZUOlt mgtuIm it s not a random graph Table 1 Comparison of Statistical Features Betneen Random Graphs and the Yeast Protein Interaction Network RAVUOM GKltI Hgt PL YEAST ER 4139 Vliolc gmpll Nodes 935 084 02 1030 970 7 31 57 Deglee 183 185098 1i4l76 No of components 163 108 8 2663 306 Giant component Nodes 0240 3S7quotquot 3369 86 Degree 207105 2 50 2 6 Clusteting coef cient X10 3 059 09 402 23quot Characteristic path length 15881176 101 114 Wagner MBE 2000 it s not a random graph Andreas Wagner Mol Biol EVOl 1871283 1292 2001 a Degree distribution 700 600 lYeast m g 500 DRandom ER g Pdocd2395 o i 5 E 400 ng quot o g x a 300 7 g a J g 200 5 z 100 H 0quot I l i l iH r T I I 1 2 3 4 5 6 7 s 9 10 Deg ree IT S ALMOST SCALEFREE POWERLAW GRAPH it s not a random graph The largescale organization of metabolic networks H Jenng B Tumhurr R Alhert Z N olmir amp AL Barah si Departmcntqutysl39lx University a NaneDamr Nam Dame Indiana 45555 USA r Department afPathblngy Nunllwmcm University Medical 671001 Chicago Ulmuis 60611 USA In a cell or microorganism the processes that generate mass energy information transfer and cellrfate speci cation are seamr lessly integrated through a complex network of cellular constimr ents and reactions However despite the key role of these networks in sustaining cel1ular tunctions their largerscale structure is essentially unknown Here we present a systematic comparative mathematical analysis of the metabolic networks of NATURE vol 407 a OCIOEER znnn V39wwnaluremm Dsedohapturose Inoshate 2000 Macmillal Drxyltnuse 57 hoshare Dery39ihrose Arphoshate Derructose Srphosphaie 22M Drnbcse Srphosphate Srphuspnur atpnarDrnbose Ldiphoshaie 105 I r r Be In hit HT 1 0quot we will it in Hit it on 7 r r In NH 4H 1039 10 PM 10 10 o 106 2 3 3 El Z 3 1o 10 10 10 10 10 10 10 K k Flame 2 Cnnnectwity dtsiributruns Ftkt for substrates at Archaeuglobus furynus arches h E cali bacteriuer c Caenorhabain s elegans eukaryulel shbwn an a tug tbg chit cauntt ng separatel the trimming int and butguing h39nks Out tar each substrate ks km corresponds to the number at reactions in which a substrate oarticinates as a product educt The characteristics mime three organisms shown in awe and the exponents 7a em miter an organisms are given in Tablet at the Supplementary ntorrnatim lit The ccnnectivtty distribution averaged over ah 43 organisms IT S ALMOST SCALEFREE POWERLAW GRAPH Random vs powerlaw Barabasi A etal Nature4112001 Wagner A Mol Biol EV01182001 Random a Scaleifree i c b a d o k log k Pk log Pk Other scalefree networks Barabasi A eta Nature4112001 Me roboli c ne rwor39k Ne rwor39k of social in rer39ac rions scien rific collaborations actors in films The Internet links physical connec rions Distributions of number of sexual partnerships have power law decaying tails and finite variance Fredrik Liljerosq Christofer R Edling H Eugene Stanleyi Y Aberg and Luis A Nunes Amaran Depnrtment ofMedion Epidemiology and Biostotistics Karolinslm Institutet SE 7 77 Stockholm Sweden ltIi1jer03ociologys zlsegt T39 Department of Sociology Stockholm Universitr 5106 9 Stockholm SwedeL Centrefor Polymer Studies Department of Physics Boston Uliivelu itif Boston MA 02215 USA Department ofCiemicnl Engineering Northwestern Universitv Evanston IL 60208 USA NATURE VOL 411 i 2 2001 thnvlr laturerom The web of human sexual contacts Promiscuous individuals are the vulnerable nodes to target in sateesex carriiiiaigns werks social networks tend to be subjective to some extent23 because the perception of what constitutes a social link may differ between individuals one Unlike clearly de ned realewnrld39 nets naires The response rate vias 59 which corresponds to 2810 respondents Two independent analyses ofnonersponse error revealed that elderly people pal ticharly women are underrepresented in the same unambiguous type of col is sexual Contact and hr sexual behaviour of a r individuals to reveal the tures of a sexualecontact that the cumulative di nLunber of different sext year decays as a scaleefr has a similar exponen females The scaleeiree ni human sexual contacts ii egic safeesex campaigns most ef cient way to pl E sexually transmitted dise Many realeworld ner a 10 10quot 102 o N D Lid l 0 Females A A Males 0 Females A Males Cumulative distribution Pun Cumulative distribution Pktm 104 i 104 10 102 10 i 10 102 Total number or partners It 101 Number of partners It 103 lot gure 2 Scalefree distribution of me number of sexual partners for females and males 3 Distribution of number of partners Ir in the prevroils 12 months Note the larger average number of partners for male respondenB tlirs difference may be due to measurement bras sbcral expectations may lead males to inflate met reported number of sexual partners Note that the distributions are both linear iriorcaong scalefree powerlaw behaviour Moreover the two curves are roughly parallel indicating srmrlar scaling exponents For females 1254 02 in the range It 4 and for males at 231 02 in the range It 5 I Distributlon ol the total number of pane ners In over respondents entire lifetimes For femala a 21 t 03 in me range Itz gt 20 and for mala a16 0 3 in the range ZOlt ltL11 lt 400 Estimates forfemala and males agree wr iin statistical uncertainty Random vs powerlaw Barabasi A eta Nature4112001 Wagner A M01 Biol EV01182001 The network of pr o reinpr o rein i n rer ac rions and o rher molecular biological networks are scalefree networks WHY Scalefree networks are be r rer OR AND Biological ne rwor39ks become scalefree due ro evolu rion Random Scalefree Removal of a randomly Removal of a random picked node node slightly increases the significantly increases average path the aVerage Path Removal of a highly All nodes are of equal connected node leads to importance drastic increase of the average path POWER LAW NETWORKS Tolerant to random quotattacksquot But more sensitive to targeted attacks Evolution of scale graphs AB model 1 Growth 2 Preferential attachment Alberts and Barabasi 2000 HerbertA Simon 1967 Evolution of graphs Growth 1 start with mo nodes 2 add a node with m edges 3 connect these edges to existing nodes at timestep t tmo nodes tm edges Evolution of graphs Preferential attachment Probability H of connection to node 139 depends on the degree k of this node Eg Zikj Rich gets richer Evolution of powerlaw graphs 1 Growth 2 Preferential attachment Rich gets richer Summary Structures of some biological network are known partially and with lots of mistakes They do not look like random graphs more like powerlaw graphs Such structures can be results of neutral evolution results of selection for robustness or other properties More connected proteins are more important Conclusion antage of mtal motel13 a WWW 440 L 1 Biological quest 88 1 I 1 i I I 1 H I l H IOHS 39 1D kkn quotEh
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